We report on progress made in a joint program of theoretical and experimental research to study the line-broadening of alkali atom resonance lines due to collisions with species such as helium and molecular hydrogen. Accurate knowledge of the line profiles of Na and K as a function of temperature and pressure will allow such lines to serve as valuable diagnostics of the atmospheres of brown dwarfs and extra-solar giant planets. A new experimental apparatus has been designed, built and tested over the past year, and we are poised to begin collecting data on the first system of interest, the potassium resonance lines perturbed by collisions with helium. On the theoretical front, calculations of line-broadening due to sodium collisions with helium are nearly complete, using accurate molecular potential energy curves and transition moments just recently computed for this system. In addition we have completed calculations of the three relevant potential energy curves and associated transition moments for K - He, using the MOLPRO quantum chemistry codes. Currently, calculations of the potential surfaces describing K-H2 are in progress.